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Draw a Venn diagram and use the given information to fill in the number of elements in each region.n(A)= 18, n(B)= 11, n(AU B)=23, n(A) = 8Complete the Venn diagram.ABU

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n(A)= 18 this item corrsponds to the number of observations inside A

n(B)= 11 this item corresponds to the number of observations inside B

n(A∪B)= 23 this item shows you the number of observations that are shared by A and B

n(A')=8 assuming A' is the complementary event of A, it indicates all observations inside the sample space that are outside A.

Total observations included in A are:

A= n(A) + n(A∪B)= 18 + 23= 41

Total of observations in B are:

B= n(B) + n(A∪B)= 11 + 23= 34

Total of observations in U

U= A + B + n(A') - n(A∪B)= 41 + 34 + 8 -23= 60

Note that I subtracted n(A∪B) one time, because is included in both A and B, i.e. is counted two times and could lead to a wrong answer.

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